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X₃₅₁₁¶

INTERSECTION OF LINES X₃X_76 AND X₆X_694

X₃₅₁₁ = crosssum of X₅₂₃ and X₂₆₇₉

X₃₅₁₁ (INTERSECTION OF LINES X₃X_76 AND X₆X_694) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3511 = INTERSECTION OF LINES X_3X_76 AND X_6X_694."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03511(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3511 = INTERSECTION OF LINES X_3X_76 AND X_6X_694 on reference triangle ABC."""
            X_3511 = eval_trilinear_point(model, A, B, C, '(a*(a**(6)*b**(4) - a**(4)*b**(6) - a**(4)*c**(6) + a**(6)*c**(4) + b**(4)*c**(6) + b**(6)*c**(4) - a**(2)*b**(2)*c**(6) + a**(2)*b**(4)*c**(4) - a**(2)*b**(6)*c**(2) - a**(4)*b**(2)*c**(4) - a**(4)*b**(4)*c**(2) + a**(6)*b**(2)*c**(2)))', ID="X_3511", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_3, X_76, 3, 76, incident=True)
            X_147 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(8) + (b**(2) + c**(2))*a**(6) - (2*b**(4) + 3*b**(2)*c**(2) + 2*c**(4))*a**(4) + (b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + c**(6))*a**(2) - b**(8) + b**(6)*c**(2) + b**(2)*c**(6) - c**(8))', ID="X_147", classes=["center", "incident"])
            X_446 = point_from_barycentrics(model, A, B, C, 5.470003, 3.521611, -7.991614, ID="X_446", classes=["center", "incident"])
            central_line(model, X_147, X_446, 147, 446, incident=True)
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center", "incident"])
            central_line(model, X_237, X_385, 237, 385, incident=True)
            return promote_point_to_top(model, X_3511)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3511 on the given reference triangle."""
            model = create_model('X_3511 = INTERSECTION OF LINES X_3X_76 AND X_6X_694')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03511(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03511.json"))
            write_center_svg(
                model_acute,
                here / "x-03511.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3511¶

X₃₅₁₁¶